Open Access
Table B1
Asymptotic models.
| Models | Expression | Remark |
|---|---|---|
| Series |
|
k
f
thermal conductivity fluid k s thermal conductivity solid Lower bound |
| Parallel |
|
k
f
thermal conductivity fluid k s thermal conductivity solid Upper bound |
| Maxwell lower bound [79] |
|
Solid medium with random distribution of small spheres |
| Maxwell upper bound [79] |
|
Solid medium with random distribution of small spheres. Dilute suspension |
| Bruggeman [80] |
|
The main approach of this theory assumes that a composite material may be constructed incrementally by introducing infinitesimal changes to an already existing material |
| Hamilton-Crosser [28] |
|
F: shape factor V: volume fraction |
| Maxwell, Comprehensive equation, from Hadley [81] |
|
Mixture of two material powders |
| Miller upper bound, |
|
Symmetric cell material
 for spherical cell shape for plate cell shape |
| Miller lower bound, |
|
Symmetric cell material.
 for spherical cell shape for plate cell shape |
| Effective Medium Theory |
|
Developed from averaging the multiple values of the constituents that directly make up the composite material. |
| Hashin-Shtrikman [29] |
|
Variational theorems applied to the derivation of bounds for the effective thermal conductivity of macroscopically homogeneous and isotropic multiphase materials |
| Krischer [63] |
|
Packed bed of spheres. A highly anisotropic structure is assumed |
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